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Contributions Towards Positioning Normal Form Method as a Tool for Analysing Future Power Transmission Grid

Abstract : Given several economic, technical and environmental constraints, today’s power systems are operated very close to their limits, which means they exhibit nonlinear behaviour more than in the past. In addition, the transfer of large amount of power over long distances common nowadays leads to nonlinear interactions, a phenomenon which challenges the traditional power system analysis tools. Furthermore, high penetration of renewable energies and the accompanying power electronics, which are evident in today's power systems, increase the nonlinearities of the systems. As a result, the well-established modal analysis tools become insufficient for the analysis of present and future power systems; making the development of alternative tools necessary.The inclusion of higher order terms in modal analysis, possible with Normal Form (NF) method, augments the information it provides, and enables better dynamic studies of systems exhibiting high nonlinear behaviour. However, NF method requires the preliminary Taylor expansion of the nonlinear system, which generates several higher order Hessian matrices and coefficients to be computed, an operation impracticable with standard methods, when considering large scale systems. In this thesis, to answer to this problem, an efficient numerical method for accelerating those computations, by avoiding the usual Taylor expansion is developed. The new computations consist in prescribing the linear eigenvectors as unknown field in the initial nonlinear system, which leads to solving linear-only equations to obtain all needed coefficients. In this way, the computation of the nonlinear model up to third order, and nonlinear modal analysis become fast, and achievable in a convenient computation time. Moreover, NF-based indices for power system stability and operation monitoring are proposed and tested on several systems.
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Nnaemeka Ugwuanyi. Contributions Towards Positioning Normal Form Method as a Tool for Analysing Future Power Transmission Grid. Other. HESAM Université, 2020. English. ⟨NNT : 2020HESAE020⟩. ⟨tel-02949258⟩

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